code: def test_decomp_3():
      T = Poly(x**2 - 35)
      rad = {}
      ZK, dK = round_two(T, radicals=rad)
      # 35 is 3 mod 4, so field disc is 4*5*7, and theory says each of the
      # rational primes 2, 5, 7 should be the square of a prime ideal.
      for p in [2, 5, 7]:
          P = prime_decomp(p, T, dK=dK, ZK=ZK, radical=rad.get(p))
          assert len(P) == 1
          assert P[0].e == 2
          assert P[0] ** 2 == p * ZK
  
imports: from math import prod
  from sympy import QQ, ZZ
  from sympy.abc import x, theta
  from sympy.ntheory import factorint
  from sympy.ntheory.residue_ntheory import n_order
  from sympy.polys import Poly, cyclotomic_poly
  from sympy.polys.matrices import DomainMatrix
  from sympy.polys.numberfields.basis import round_two
  from sympy.polys.numberfields.exceptions import StructureError
  from sympy.polys.numberfields.modules import PowerBasis, to_col
  from sympy.polys.numberfields.primes import prime_decomp, _two_elt_rep, _check_formal_conditions_for_maximal_order
  from sympy.testing.pytest import raises
label_desc: Use image node_id 6 for calling a global function with example usage: test_decomp_3() without return types